Tsunami wave impact on walls & beaches.

Tsunami wave impact on walls & beaches

• Numerical predictions

• Experiments

– Small scale;

– Large scale.

Numerical Free-surface models

Airy, Stokes II

Stokes III-V, stream function Fully nonlinear

NLSW, Boussinesq 3rd _{generation spectral}

Large bodies: ships, FPU, fixed offshore platforms Offshore wind farms, tidal machines, WECs

Oscillations: harbours/Lakes, sloshing, runup/overtopping MetOcean conditions & Resource assessment

RANS VOF

SPH + subgrid scale Lattice Boltzmann

Commercial: Flow3D, Xflow, WAMIT, ANSYS Aqwa, WAM, SWAN. Research: COULWAVE, FUNWAVE, SWAN, MIKE Inviscid models Viscous models Applications Solvers

• Numerical investigations of

VIV & free surface water

waves: continuum mechanics

models.

• Bridge length/time scales

btw. micro and continuum

mechanics level.

• Identify numerical model

approach aiming at:

1. FSI/High Re problems; 2. Fr > 1 problems;

3. Nonlinear free surface water wave problems;

4. Wave-seabed interactions; 5. Water wave bluff body

interactions?

VIV = Vortex Induced Vibrations; FSI = Fluid Structure Interaction. Traditional research models:

Alternative research models:

Comparison of numerical methods

FD σ-method RANS VOF LBM SPH PFEM

Grid dependent soln. yes yes yes no yes

Wave continuous yes yes yes yes yes

Nonlinear waves yes yes yes yes yes

Free-surface algorithm yes yes Yes/no no yes

Wave breaking no yes Yes (?) yes yes

Bubble break-up no no yes no no

Poisson freedom yes no Yes (no) yes no

Viscosity ok ok challenge challenge ok

BC simple ok no yes no no

FSI/arbitrary

geometry/topologies

no yes yes yes yes

Efficient parallelization no no Yes/no ? ?

CPU efficiency Ok/small domains no Ok so far no ?

• Why….

• Breaking wave predictions,

• Local free-surface model and coupling effects.

• “….knowledge and methods established in gas dynamics can be transferred directly to

long water waves.” Mei, “The applied dynamics of ocean surface waves”, 1989;

• “…..impossible to doubt a close connection btw. mathematical analogy of gas dynamics

and the structure underlying long surf on beaches”. Meyer, Physics of Fluids, 1986;

• Wehausen & Laitone, “Surface Waves”, 1960;

• Stoker, “Water Waves”, 1957;

• Courant & Friedrichs, “Supersonic flow and shock waves”, 1948.

• Einstein, H. & Baird, “…surface shock waves on liquids & shocks in compressible gases.”

CalTech Report, 1946.

• Riabouchinsky, 1932.

L. Boltzmann

On the Analogy btw. Water waves and gas dynamics theory:

Kinetic modeling approach:

Non-breaking wave models – CPU based

• Salmon 1999. Journal of Marine Research 57, 503-535.

• Ghidaoui et al. 2001. Intl. J. for Num. Methods in Fluids 35. • Buick & Greated 2003. Physics of Fluids 10 (6), 1490-1511. • Zhou 2004. LB Methods for Shallow Water Flows. Springer. • Zhong et al. 2005. Advances in Atmos. Sciences 22(3).

• Ghidaoui et al. 2006. J. Fluids Mechanics 548. • Frandsen 2006. Intl. Journal of CFD 20 (6).

• Que & Xu 2006. Intl. J. Num. Meth. in Fluids 50. • Thommes et al. 2007. Intl. J. Num. Meth. in Fluids.

• Frandsen 2008. Advanced Numerical Models for Simulating

Tsunami Waves & Runup. Advances in Coastal & Ocean Engrg. World Scientific (10).

• ...

Observations

• Non-breaking wave model:

1. NLSW equations;

2. No free-surface algorithm.

• Breaking wave model:

1. Navier-Stokes equations;

Lattice Boltzmann Model

• Fluid motion governed by Navier-Stokes eqn.; • Particles move along lattice in collision process;

• Collisions allow particles to reach local equilibrium;

• Discretized particle velocity distribution function; • 3D: ex. 19 or 27 velocities on a cubic lattice;

• Hydrodynamic fields:

total depth, velocity and pressure.

Continuum Molecular Meso α β γ 12 13 7 10 8 9 17 16 18 15 0 4 11 3 6 2 1 5 14 y z x k j i

Collision Integral

• Single time relaxation,

-

LBGK model, after Bhatnagar et al. (1954) ;

• Multi Relaxation Times, MRT models.

Approximations:

Original Boltzmann Equation

L. Boltzmann

Lattice Boltzmann Model in Shallow water

LBGK model example

2 2 2 0 0 0 0 2 2 ( ) ( ) ( ) 2 eq i i i g h t h t f h u u x x               2 2 2 0 0 0 1,2 2 2 ( ) ( ) ( ) ( ) 4 2 2 eq i i i i i g h t h tu h t f c u u x x x                 2 0 0 i i f h     

 Discrete velocity model (D1Q3)

 The macroscopic variables

2 0 0 1 ( ) i i i u c f h    



j f 1 f 2 f 1 f2 (1 − )α f₁ (1 − )α f₂ f 2 α f 1 α x + xΔ t + tΔ t + c _ c f 2 f1 ( = c ) Δ (x + 2x) j x t

(Soln.: 0. Initial conditions; 1. Calculate feq_{; 2. Compute f} i.)

•

Free-surface: no algorithm is prescribed in

non-overturning wave model;

•

Wave run-up: dry/wet phase (h 0):

 Automatically handled (i.e., thin film: h~10

-5

_m);

 Shoreline algorithm;

 “Slot method”.

z x L z₀ h₀ h_b 

h

₀

/L

₀

0 , ε = a/h

₀

= O(1)

Z₀ = 5000 m ∂h_b/∂x = 1/10 L = 50 km

•

Problem Set-up

Near-shore view:

Domain view:

 FDLB model

Validation

 FDLB model

−400 −200 0 200 400 −20 −10 0 10 20 x [m] u s [m/s] −400 −200 0 200 400 −20 −10 0 10 20 x [m] u s [m/s]

Other initial wave forms

−400 −200 0 200 400 −20 −10 0 10 20 x [m] u s [m/s] −400 −200 0 200 400 −20 −10 0 10 20 x [m] u s [m/s] A B C _D −0.050 5 7 x 104 −4 0 10 x [m] ζ [m] −0.050 5 7 x 104 −10 0 4 x [m] ζ [m] −0.050 5 7 x 104 −4 0 10 x [m] ζ [m] A B C D

Experimental set-up and definitions 1 m /4 b/4 b /2 l /2 l /2 x y 1 3 2 Swa y Surge 1 m b b 1 h 2 U₀ h₀ u_y ζ h Wave gauge

Large sway motion

a

_h

/b=0.02

_a

_h

_/b=0.05

_a

_h

_/b=0.1

h

₀

/b=0.05

Fr₁=1.1 h₁/h₂=1.6 Fr₁=1.3 h₁/h₂=2.2 Fr₁=1.4 h₁/h₂=6.9

sway

heave

heave

+

sway

h₀/b = 0.2:

Numerical simulations in Frandsen, JCP (2004)

Free-Surface experiments in small tanks

0.8 1 1.2 0 0.2 0.4 ω_h/ω 1 ζ max /b 0.8 1 1.2 0 0.2 0.4 ω_h/ω 1 ζ max /b

Horizontal moving tank with forcing frequency ω_h -x -, Analytical 3rd _{order solution;}

-o-, numerical nonlinear potential flow soln,

a_h/b = 0.003 (Frandsen, JCP’04);

- - , experimental solution (a_h/b = 0.003);

, experimental solution (a_h/b = 0.006);.

h₀/b = 0.2 h₀/b = 0.6

Sloshing in tank: physical vs. numerical test soln

2 n₁

n

ζ

hs still water level

Δσ = 1 X Δ = 1 2 m₁ m (b) (a) σ X mapping b z Initial profile x

●

, wave breaking

Free-surface VOF LB model

• Free-surface algorithm using Volume of Fluid (VOF) method (Ginzburg & Steiner, 2002)

• D3Q27 lattice (recovers the Navier-Stokes equations) • Mesh: Structured, Octree grids

• Adaptivity: mesh adapts to the wake while the flow develops. (constraints on the local dimensionless vorticity.)

• Large Eddy Simulation (local wall adapting eddy viscosity model) • Multiple Relaxation Time

Wave runup on beaches

Wave tank: 37.7 m  0.61 m  0.39 m After Synolakis, JFM (1987)

LB solution:

Smooth Beach: 1:19.85 Runup height vs. wave height

H/d =0.5, R/d = 1.511 LB VOF solns

Expériences

Large Scale Testing

04

• Depth/width: 5 m; Length: 120 m • Water depth: 2.5 - 3.5 m

• Wave period: 3 - 10 s.

• Wavemaker (piston): max. stroke length/velocity: 4 m, 4 m/s. • Initial conditions:

Regular/ irregular waves & user-defined functions, e.g., landslide & earthquake-generated tsunami. • The flume is designed for modeling the interactions of

waves, tides, currents, and sediment transport.

• Instrumentation: ADP, ADV, Aquadopp, turbidity, water level -and pressure sensors. multibeam system (bathymetry).

Expériences

Wave impact on walls

04 octobre 2013

Large Scale Testing

04

~ 10 m

Concluding thoughts

Near-shore Hydrodynamic

Models

• Compatible with other nonlinear shallow water solvers; • Hybrid models to bridge length/time scales;

• Assist in design of coastal/harbor structures;

• Simplified models in the context of warning systems,

evacuation and inundation mapping.

Kinetic approaches when viscosity and complex fluid mixing and structural response as coupled interactions matters.

Questions?

Jannette B. Frandsen http://lhe.ete.inrs.ca 27 Mar. 2014